In an interview with New York radio host John Catsimatidis airing Sunday, Giuliani claimed that Mueller's team has known since "May or June" that there is no evidence to support the allegation that members of Trump's campaign knowingly worked with Russians during the 2016 election.

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“It should have been wrapped up probably in May or June. That’s when they figured out they had no evidence of collusion," Giuliani asserted, adding, "Collusion is not a crime, by the way."

"You have to show a conspiracy to hack [the Democratic National Committee]," he added. "They don’t have any evidence of that — which is the reason they don’t submit a report, because they are embarrassed."

Giuliani went on in the interview to urge Mueller to release his final report while appearing to suggest that the special counsel will not have evidence required to bring criminal charges against the president.

"So, I am challenging them: It’s time to put up or shut up. It’s time for them to submit a report," Giuliani said. "They don’t have, as we would say in New York, a damn thing.”

Giuliani, who joined the president's legal team responding to the special counsel's inquiries earlier this year, has repeatedly urged Mueller's team to wrap up its investigation into Trump campaign associates and Russia.

The former New York City mayor also called this week for Mueller, who formerly served as director of the FBI, to be investigated for destruction of evidence related to missing text messages detailing conversations between FBI employees Peter Strzok and Lisa Page, who were removed from the investigation over alleged anti-Trump bias.

“Mueller should be investigated for destruction of evidence for allowing those text messages from Strzok to be erased, messages that would show the state of mind and tactics of his lead anti-Trump FBI agent at the start of his probe,” Giuliani told Hill.TV this week.